Optimal Shape Design for Parabolic System and Two-Phase Stefan Problem
Sergei P. Ohezin · Birkhäuser Basel eBooks · 1992
In this paper we consider the application of the domain control theory in parabolic systems for the approximation of two-phase one-dimensional Stefan problem [ 1 ]. In this approach the role of the control function is carried out by the free-boundary (or interface). We use the shape penalty method [ 2 , 3 ] and investigate the corresponding approximation family of control bilinear systems and prove the theorem about uniform approximation. It is shown that classical solution of Stefan problem is a limit of the approximation solutions.